Question

Aluminium crystallizes in a cubic close packed structure. Its metallic radius is $125pm$.
i) Calculate the edge length of unit cell
ii) How many unit cells are there in $1.00c{m}^3$ of aluminium?

• A. $354pm,2.41\times {10}^{22}$
• B. $355pm,3.41\times {10}^{20}$
• C. $356pm,4.41\times {10}^{21}$
• D. $357pm,5.41\times {10}^{23}$

Answer 1

The correct option is A $354pm,2.41\times {10}^{22}$

For a $FCC$ or $CCP$ unit cell,

$4r=\sqrt{2}\times a$ or $a=\frac{4r}{\sqrt{2}}=354pm$

$\because$ Volume of one unit crystal $=a^3=44361864\times {10}^{-30}c{m}^3$

$\therefore$ No. of unit cells in $1c{m}^3$ aluminium = $\frac{1\times {10}^{30}}{44361864}=2.41\times {10}^{22}$